DHA Service Access and Coverage Indicators

1 Aim

Birth and death registration may be incomplete due to the inaccesibility of home affairs offices registration occurs. A potential barrier to registration may be the distnace neede to travel. We aim to determine the proportion of the population within reasonable distances of home affairs offices.

2 Methodology

Shape files were taken from … and district names were standardised using an author-made package {NMCleaner}. Poulation estimates were taken from StatsSA (published 2025), down to the district level. One district was not matched, but will need to run all code again later (Buffalo City).

The coordinates of home affairs offices were taken from Tom Moultrie’s .dta file. This appears to omit offices in hospitals.

To determine the number of people within a certain distance of a home affairs office we explored options before finalising with the third.

  1. We measured the distance between the nearest paris of offices. We took the median half distance as the distance each person in the population would need to travel to their nearest offices. The median half distance between each office within each district was assumed to apply to all populations in the district, this however assumes that should two HA offices be far apart, then all population is out of reach of the office, this underesitmated the coverage, especially in rural areas.
  2. We then created a 1km grid pattiern. We assumeed uniform distribution of population within each district based on that districts population and distributed to these grid points. This, while not knocking out rural areas completely, ignores the fact that populations are likely to be clustered.
  3. The third method assumes that population is clustered around DHA offices, uniformly across rural and urban areas (same distribution around all offices, in proportion ot the districts population). Other than a visual inspection of the map, I don’t have data to verify the decay of population density around HA offices. In addition, the main with this assumption is that it assumes that all population nodes are situated around DHA offices, which is unlikely to be true in rural areas.

The second and third methods utilise population density models. Three models are available for distributing population across grid points:

1. Uniform Distribution (method 2) \[ w_i = 1 \]

2. Inverse Power Model (method 3) \[ w_i = \frac{1}{(d_i + 1)^{\alpha}} \]

where \(d_i\) is the distance (km) from grid point \(i\) to the nearest office, and \(\alpha\) is the decay parameter (default 1.5). The +1 offset prevents division by zero.

3. Exponential Decay Model (not used) \[ w_i = e^{-\alpha \cdot d_i} \]

2.0.1 Population Allocation

Weights are normalised within each district to preserve total district population:

\[ \hat{w}_i = \frac{w_i}{\sum_{j \in d} w_j} \]

The population at each grid point is then:

\[ P_i = P_d \cdot \hat{w}_i \]

where \(P_d\) is the total population of district \(d\).

2.0.2 Distance-to-Access Metrics

Grid points were plotted in a 1km grid pattern. We summed the population value of each grid within the specified distance bands (10km and 20km) to get the proportion of the district population within each distance band.

2.0.3 Limitations

  • Population is modelled, not observed at sub-district or enumeration area level
  • Distance are straigh-line, not road-network or travel-time
  • Office capacity and service quality are not accounted for
  • Satellite offices are not recorded in the dataset.

Without trying to assume too much more, I would suggest we request enumeration area census data (even if it is old and imperfect) to get an idea of how population is distributed around DHA offices and also to identify population clusters without offices.

3 National overview maps

3.1 Population distribution (district total)

3.2 Number of DHA offices (district total)

3.3 Modelled population distribution around offices

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Table 1

District

Total Population

Population within 10 km

% Population within 10 km

Population within 20 km

% Population within 20 km

Median Distance to Nearest DHA Office (km)

Alfred Nzo

935,303.24

455,653.79

48.71723

743,055.57

79.44542

10.402110

Amajuba

610,840.87

248,304.97

40.64970

412,243.37

67.48785

6.721991

Amathole

792,612.28

384,503.90

48.51097

624,102.29

78.73992

13.710934

Bojanala Platinum

1,985,081.47

973,231.05

49.02726

1,498,577.12

75.49197

6.631565

Buffalo City

0.00

0.00

0.00

6.645311

Cape Winelands

1,014,431.61

393,345.32

38.77495

660,490.34

65.10940

22.244051

Capricorn

1,412,657.09

704,095.36

49.84192

1,090,471.68

77.19295

6.588786

Central Karoo

77,156.77

19,337.85

25.06306

33,406.26

43.29660

61.232752

Chris Hani

717,288.80

284,460.44

39.65773

477,556.61

66.57801

18.530152

City of Cape Town

5,030,496.59

4,099,371.70

81.49040

4,680,808.63

93.04864

5.701034

City of Johannesburg

5,900,321.36

5,628,983.35

95.40130

5,892,801.12

99.87255

4.655293

City of Tshwane

4,038,060.52

2,807,261.12

69.52004

3,797,729.06

94.04834

6.261707

Dr Kenneth Kaunda

807,057.02

306,765.87

38.01043

534,494.42

66.22759

26.442373

Dr Ruth Segomotsi Mompati

474,901.42

126,706.75

26.68064

226,657.34

47.72724

37.381759

Ehlanzeni

1,928,692.28

949,462.10

49.22828

1,514,775.37

78.53899

14.563862

Ekurhuleni

4,059,057.15

3,606,628.50

88.85385

4,026,309.04

99.19321

4.287919

Fezile Dabi

536,755.09

210,021.56

39.12801

354,981.92

66.13480

25.841309

Frances Baard

438,828.63

252,121.61

57.45332

344,875.36

78.58999

6.517864

Garden Route

673,192.44

231,968.78

34.45802

359,566.57

53.41215

26.215135

Gert Sibande

1,367,512.57

499,243.04

36.50738

865,389.43

63.28201

23.991729

Harry Gwala

507,708.07

244,651.59

48.18745

393,554.66

77.51593

14.683459

Joe Gqabi

354,930.59

120,698.07

34.00611

201,178.45

56.68107

26.070329

John Taolo Gaetsewe

296,434.12

60,903.61

20.54541

105,421.63

35.56326

58.748156

King Cetshwayo

992,551.26

584,674.80

58.90626

878,507.60

88.51005

11.117175

Lejweleputswa

698,356.31

237,432.69

33.99879

415,209.16

59.45520

21.777022

Mangaung

857,972.98

368,652.30

42.96782

569,401.61

66.36591

7.357610

Mopani

1,266,833.75

637,248.98

50.30249

965,505.48

76.21406

11.449517

Namakwa

129,514.62

18,622.61

14.37877

32,227.66

24.88342

101.611559

Nelson Mandela Bay

1,263,632.35

913,989.64

72.33034

1,177,353.23

93.17213

5.560911

Ngaka Modiri Molema

916,906.71

356,376.61

38.86727

585,529.12

63.85918

11.025078

Nkangala

1,779,928.23

915,034.71

51.40852

1,379,989.56

77.53063

14.948017

O.R. Tambo

1,623,984.18

901,159.23

55.49064

1,383,466.86

85.18968

11.402136

Overberg

329,835.08

129,158.89

39.15863

214,444.59

65.01570

29.774281

Pixley ka Seme

219,155.39

44,534.82

20.32111

78,796.01

35.95440

60.644279

Sarah Baartman

527,417.58

137,390.39

26.04964

236,924.35

44.92159

36.350580

Sedibeng

1,061,184.78

698,345.41

65.80809

956,981.76

90.18050

5.241618

Sekhukhune

1,333,431.61

623,523.74

46.76083

1,030,150.20

77.25557

13.957115

Thabo Mofutsanyana

810,097.04

281,905.92

34.79903

474,806.88

58.61111

21.412738

Ugu

831,709.41

410,976.35

49.41345

648,175.00

77.93287

15.690580

Umzinyathi

607,975.36

279,572.67

45.98421

481,574.42

79.20953

20.312587

Vhembe

1,527,097.27

814,783.91

53.35508

1,210,957.63

79.29800

11.353646

Waterberg

826,172.40

270,753.13

32.77199

469,022.86

56.77058

20.385642

West Coast

502,575.67

158,658.18

31.56901

266,240.56

52.97522

53.950602

West Rand

1,046,309.52

595,362.01

56.90114

881,712.99

84.26885

6.530380

Xhariep

136,652.09

32,346.18

23.67046

58,520.08

42.82414

32.967104

ZF Mgcawu

295,250.15

65,364.51

22.13869

109,046.04

36.93344

49.658992

Zululand

901,274.60

416,978.23

46.26539

696,858.99

77.31928

14.419205

eThekwini

4,374,202.14

3,566,220.60

81.52848

4,314,338.52

98.63144

4.116189

iLembe

742,038.00

487,512.25

65.69910

715,374.15

96.40667

14.468760

uMgungundlovu

1,220,477.11

558,332.70

45.74708

974,950.39

79.88273

18.124755

uMkhanyakude

711,366.32

369,937.77

52.00383

571,470.34

80.33419

20.035972

uThukela

732,104.09

233,310.61

31.86850

401,013.65

54.77550

28.928896

Total

62,225,325.98

37,715,880.17

60.61178

51,016,995.93

81.98751

13.856925

3.4 Interactive map of DHA offices and population coverage